Time-varying Sampling Research Articles

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

A novel model-based Cauchy-Schwarz divergence condition indicator for gears monitoring during fluctuating speed conditions

Gear monitoring and fault diagnosis are vital for preventing accidents and minimizing economic losses in transportation and industrial systems. Traditional methods use vibration sensors and a two-stage analysis approach: preprocessing data to remove noise and extract relevant components, and generating a condition indicator to detect behavioral anomalies in the gears over time.Time synchronous averaging is a notable tool for monitoring gears at constant speeds. Such a tool filters sensor signals and extracts rotation-related components by using statistical measurements as condition indicators. However, it has limitations in scenarios with time-varying sampling rates and fluctuating speeds, where statistical measures may not fully capture changes in system parameters.This article proposes a novel methodology for monitoring gears in multivariate rotordynamical systems under fluctuating speed conditions. The method integrates time synchronous averaging, system identification algorithms, and statistical tools. It generates a time-synchronous average signal considering speed fluctuations, computes a state–space model of gear behavior in healthy states, extracts residual data from a data-driven model, and generates a condition indicator based on the Cauchy–Schwarz divergence.The proposed methodology was evaluated using experimental data from three rotor dynamical setups under different operational conditions. Validation showed its effectiveness, especially under high-load conditions with significant speed fluctuations.

A likelihood-based adaptive CUSUM for monitoring linear drift of Poisson rate with time-varying sample sizes

Several weighted cumulative sum (CUSUM) and adaptive CUSUM (ACUSUM) control charts have been developed to address the challenge of time-varying sample sizes in detecting the incidence rates of Poisson count data. However, the known post-drift parameters in the CUSUM chart make it less realistic. Additionally, the adaptive component in the ACUSUM chart cannot integrate with time-varying sample sizes naturally. Furthermore, the existing charts predominantly address step drift, neglecting linear drift. Hence, this study introduces a Poisson ACUSUM chart that considers both linear drift and integration issues. Detailed comparisons are made among the proposed control chart, CUSUM control charts, and other ACUSUM control charts. Results demonstrate the proposed method's superior robustness and ability to effectively detect small drifts. Finally, the empirical results of the mortality data are employed to further validate the effectiveness of the proposed method.

Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes

Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes

Data-Driven Practical Cooperative Output Regulation Under Actuator Faults and DoS Attacks.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

Adaptive discrete mapping of dynamic nanomechanical property of soft materials on atomic force microscope

In this paper, an adaptive discrete nanomechanical mapping (A-DNM) technique is proposed for mapping time-varying nanomechanical properties of soft samples using atomic force microscope (AFM). Mapping time-varying nanomechanical properties is needed to investigate samples such as live cells undergoing dynamic evolutions. However, the existing methods based on continuous scanning are either too slow to capture time-elapsing variations of the sample over the entire sampled area, or only capable of mapping a small sample area. Contrarily, we propose to extend a discrete nanomechanical mapping scheme where only a set of chosen discrete locations (points of interests, POIs) are measured, thereby, dramatically increasing the number of measurements acquired at these POIs during the dynamic evolution of the sample occurring in minutes or faster. Specifically, through the proposed A-DNM approach, two challenges are addressed: First, the effect of time-varying sample topography during the nanomechanical evolution is accounted for by updating the estimation of the sample height at each POI during the mapping and compensating for it in the cantilever transition and engagement process. Secondly, an adaptive planning of the mapping sequence is proposed to adjust the distribution of the measurements between the POIs to accomodate the sample dynamic evolution. A POI-dynamics index is introduced to estimate the relative speeds of the nanomechanical evolutions at the POIs based on the measured data, and then online assign more measurements to those POIs of faster nanomechanical evolutions. The proposed approach is demonstrated through an experiment of mapping nanomechanical evolution of a poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) polymer undergoing crystallization process.

A self-starting non-restarting CUSUM chart for monitoring Poisson count data with time-varying sample sizes

Many studies have focused on monitoring the incidence rate of Poisson count data with time-varying sample sizes, with control charts being widely used. However, almost all of the existing reports mainly focus on solving the problem of time-varying sample sizes. Rare attention is paid to the real-life problems where the data cannot restart. Besides, these studies aim at Phase II with the in-control parameters known, which is unrealistic in real applications. As far as we know, there is no research on the non-restarting and unknown in-control parameters control charts, but it is essential and critical for extending applications of control charts. To address these limitations, this study offered two self-starting non-restarting cumulative sum (CUSUM) control charts based on the modified test to monitor the incidence rate of non-restarting Poisson data with time-varying sample sizes. The methods can be applied to other control charts and take into account both Phase I and Phase II without assumptions of time-varying sample sizes. Moreover, the monitor can be carried out with small Phase I samples. Simulation results show that the second control chart proposed in this study (SSNR-CUSUM-P2) is optimal compared to the common non-restarting control chart (E) and the first control chart proposed in this study (SSNR-CUSUM-P1). The SSNR-CUSUM-P2 chart has the highest similarity to the control chart with known parameters (T) in both post-outbreak false alarm rate and outbreak time point set. Finally, a dataset on German measles patients and a dataset on US employment are used to illustrate the application of the methods.

Event-triggered H ∞ control of complex dynamical networks subject to stochastic cyber-attacks by new two-sided delay-dependent LKF functional

ABSTRACT This article deals with the problem of event-triggered control of complex dynamical networks (CDNs) subject to stochastic cyber-attacks and random coupling delays. Hackers may abuse the system by injecting malicious activity into communication networks. Two types of non-linear functions for cyber-attacks, time-varying coupling delays, respectively, and a set of random variables satisfying the Bernoulli distribution are proposed. Against complex dynamical networks, an attacker has the capacity to change the transmitted data. So the traditional control method can be a major challenge, and it is essential to respond to cyber-attacks of this kind. An event-triggered mechanism (ETM) was implemented to avoid losing limited bandwidth. The input delay method is then used to build a time-varying sample under stochastic cyber-attacks. The stability criterion of the developed system model and the display expression of control parameters are then established using a new two-sided delay-dependent Lyapunov–Krasovskii functional (LKF) and linear matrix inequality (LMI) techniques. Lastly, two numerical examples, including the inverted pendulum application, are presented to illustrate the effectiveness and feasibility of the derived theoretical results.

On Sontag’s formula for the sampled-data observer-based stabilization of nonlinear time-delay systems

In this paper, a new methodology for the design of sampled-data dynamic output feedback (DOF) stabilizers for control-affine nonlinear time-delay systems is proposed. In particular, the methodology here developed is based on the Artstein’s theory of control Lyapunov functions and related Sontag’s formula, here extended, for the first time in the literature, to the case of DOF controllers. Firstly, the new notion of Steepest Descent Error Dynamics (SDED) is introduced and used to suitably re-formulate the well-known Sontag’s universal formula for the case of DOF controllers. Then, it is shown that, under suitably fast sampling, a proposed sampled-data DOF controller based on the new provided version of Sontag’s universal formula ensures the semiglobal practical stability of the related sampled-data closed-loop system. Time-varying sampling intervals, as well as the intersampling system behavior, are taken into account. In the theory here developed, the case of delay-free systems is addressed as a special case. Applications are presented for the validation of the proposed theoretical results.

Identifying and interpreting regional signals in tree-ring based reconstructions of snow avalanche activity in the Goms valley (Swiss Alps)

One of the purposes of dendrogeomorphic studies is to provide long and continuous reconstructions of mass movements and to detect climate-induced trends in process activity. The development of regional chronologies—in which information from different sites are aggregated—is often needed to identify process–climate relations and to overcome local-scale specificities, sparse data available for individual sites and to extract a signal that is common to a larger region and possibly driven by past climate fluctuations or large-scale environmental changes. Yet, such chronologies are scarce and consensus neither exists on how to compile local data at the regional scale nor on the methods to be used to extract a common signal. In the case of snow avalanches, existing regional tree-ring studies typically included less than ten paths, and they discriminated years of high/low avalanche activity based on a regional index representing the proportion of disturbed trees in any given year. However, such an index does not account for potential non-stationarities in local tree-ring reconstructions such as e.g., time-varying sample size, decreasing dendrogeomorphic potential of trees after the occurrence of an extremely large, devastating avalanche or socio-environmental changes. Here we combine a dendrogeomorphic approach to reconstruct snow avalanche events in 11 paths located in the Goms valley (Swiss Alps) with an innovative statistical modelling approach. For each path, we compute reconstructions using a 4-step procedure to disentangle potential effects of snow avalanches from disturbance pulses in trees caused by climatic or other exogenous factors. We then process the regional dataset (spanning the period 1766–2014) within a Bayesian hierarchical spatio-temporal framework specifically designed to homogenise time series of avalanche events by i) removing trends related to the decreasing number of living trees back in time and ii) inferring robust trends in mean annual/regional avalanche activity in time and space. This contribution has the merit to introduce a methodological approach allowing rigorous extraction of common, average avalanche signals from snow avalanche paths characterized by heterogeneous process activity. Despite its stringency, we show that 11 avalanche paths may not suffice to yield a signal that is independent from the selection of couloirs. As a result, the approach also does not highlight a clear climatic control of snow avalanche activity but rather points to a complex, yet combined impact of afforestation and management strategies on reconstructed avalanches.

What Is the Active Prevalence of COVID-19?

Abstract We provide a method to track the active prevalence of COVID-19 in real time, correcting for time-varying sample selection in symptom-based testing data and incomplete tracking of recovered cases and fatalities. Our method only requires publicly available data on positive testing rates in combination with one parameter, which we estimate based on a representative randomized sample of nearly 10,000 individuals tested in Utah in May and June 2020. We validate our method using external studies in Indiana in April 2020 and two counties in Utah in March 2021. In all three locations and times, our estimates of latent prevalence are within the 95 percent confidence intervals of prevalence estimates from randomized testing. Applying our method to all 50 states, we show that true prevalence is 2-3 times higher than publicly reported.

On Semi-Global Exponential Stability Under Sampling for Locally Lipschitz Time-Delay Systems

In this article, the stability preservation problem for locally Lipschitz nonlinear time-delay systems, by emulation of continuous-time dynamic output feedback controllers, is studied. Sufficient Lyapunov-like conditions are provided such that, by suitably fast sampling, the Euler emulation of continuous-time dynamic output feedback controllers ensures the semiglobal exponential stability of the related sampled-data closed-loop system. If other emulation schemes than the Euler one are used, practical semiglobal exponential stability is guaranteed, with arbitrarily small final target ball, by suitably fast sampling. The intersampling system behavior, as well as time-varying sampling intervals, is taken into account. In the provided results, the delay-free case is included as a special case. The practical applicability of the provided results is shown through the study of a nonlinear chemical reactor system with recycle and a glucose–insulin system.

Asymptotically stable optimal multi-rate rigid body attitude estimation based on lagrange-d'alembert principle

<abstract><p>The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.</p></abstract>

Covariance recovery for one-bit sampled stationary signals with time-varying sampling thresholds

One-bit quantization, which relies on comparing the signals of interest with given threshold levels, has attracted considerable attention in signal processing for communications and sensing. A useful tool for covariance recovery in such settings is the arcsine law, that estimates the normalized covariance matrix of zero-mean stationary input signals. This relation, however, only considers a zero sampling threshold, which can cause a remarkable information loss. In this paper, the idea of the arcsine law is extended to the case where one-bit analog-to-digital converters (ADCs) apply time-varying thresholds. Specifically, three distinct approaches are proposed, investigated, and compared, to recover the autocorrelation sequence of the stationary signals of interest. Additionally, we will study a modification of the Bussgang law, a famous relation facilitating the recovery of the cross-correlation between the one-bit sampled data and the zero-mean stationary input signal. Similar to the case of the arcsine law, the Bussgang law only considers a zero sampling threshold. This relation is also extended to accommodate the more general case of time-varying thresholds for the stationary input signals.

Distributed Resilient Secondary Control for DC Microgrids Against Heterogeneous Communication Delays and DoS Attacks

In this article, a cooperative resilient control method for dc microgrid (MG) is proposed to dispel the adverse influences of both communication delays and denial-of-service (DoS) attacks. To avoid that the sampling period is captured by intelligent attackers, a new time-varying sampling period, and an improved communication mechanism are first introduced under the sampling control framework. Based on the designed sampling period and communication mechanism, a resilient secondary controller is designed. It is theoretically shown that the developed method can achieve the goals of bus voltage restoration and current sharing even in the presence of both DoS attacks and heterogeneous communication delays. Finally, a dc MG test system is built in a controller-hardware-in-the-loop testing platform to illustrate and verify the effectiveness of our developed method against both communication delays and DoS attacks.

(Invited) Accelerating Electrochemistry: The Development of Rapid Impedance Methods and High-Throughput Screening of Novel Oxide Electrodes for Fuel Cells and Electrolyzers

As electrochemical technologies rise to ever greater prominence in the global energy landscape, new techniques to accelerate the discovery, design, and characterization of novel electrochemical materials and devices are needed. Motivated by this opportunity, here we present our recent work in the development of novel rapid multi-dimensional impedance characterization using the Distribution of Relaxation Times (DRT) combined with high-throughput impedance-based screening of electrocatalysts for ceramic fuel cells and electrolyzers, both of which offer opportunities to accelerate electrochemical materials research and development.The DRT has been established as a versatile tool for analysis of electrochemical impedance spectroscopy (EIS) data, providing insight into the relevant electrochemical processes of fuel cells, batteries, and other devices without the constraints of an a priori model. Here, we present a method for obtaining the DRT directly from rapid time-domain measurements. This technique provides the DRT on a time-scale that is 1-2 orders of magnitude faster than conventional EIS measurements, and opens new avenues for characterization and analysis that are inaccessible and/or impractical with conventional EIS. We demonstrate how this technique can be used to construct multidimensional DRT maps as a function of variables such as applied bias, temperature, changing gas conditions, or state-of-charge (Figure 1). In addition, the model can be adapted to account for time-varying sample states, enabling meaningful analysis of unstable samples and transient phenomena such as equilibration or degradation processes. Finally, we demonstrate how hardware sampling-rate limitations can be overcome via hybrid frequency- and time-domain measurements to scan a broad range of timescales without sacrificing measurement speed. The capability of this method to resolve the DRT along additional dimensions promises to enhance the interpretability of the DRT and provide new insight to guide materials and device optimization.We then discuss how rapid impedance characterization and analysis methods can be coupled to combinatorial thin-film synthesis and high-throughput automated characterization to investigate a large family of catalytically-active triple-ionic-electronic conducting oxide perovskite materials based on the Ba(Co,Fe,Zr,Y)O3-δ (BCFZY) compositional system, which show great promise for catalyzing the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) for ceramic fuel cells and electrolyzers (Figure 2). In total, we collected and analyzed more than 2,500 impedance spectra from three combinatorial thin-film electrode libraries, comprising 432 distinct compositions. These libraries were synthesized by pulsed laser deposition and measured at three temperatures under two different gas atmospheres, enabling a new scientific insight into the trends governing electrochemical performance. Our combinatorial experiments demonstrate that Co-rich compositions achieve the lowest overall polarization resistance under both dry air and humid N2, while high Fe content may impede the performance at low-to-intermediate temperatures. Reuslts from the combinatorial experiments are supported by isotope-labled SIMS trace diffusion studies as well as by protonic-ceramic fuel cell and electrolysis cell testing of both symmetric cells and full cells that incorporated select compositions of interest. Hierarchical Bayesian analysis indicates that the performance-limiting process depends on the chemical composition, measurement temperature, and atmospheric humidity. Thus, by combining rapid analysis methods with combinatorial experimentation, we achieve a composition map of the condition-dependent electronic properties of materials in the BCFZY perovskite family for application as air electrodes in protonic ceramic fuel cell and electrolyzers. Figure 1

Covariance Recovery for One-Bit Sampled Non-Stationary Signals With Time-Varying Sampling Thresholds

The recovery of the input signal covariance values from its one-bit sampled counterpart has been deemed a challenging task in the literature. To deal with its difficulties, some assumptions are typically made to find a relation between the input covariance matrix and the autocorrelation values of the one-bit sampled data. This includes the arcsine law and the recently proposed modified arcsine law which unleashes a promising performance in covariance recovery by taking advantage of time-varying sampling thresholds. However, the modified arcsine law also assumes input signals are stationary, which is typically a simplifying assumption for real-world applications. In fact, in many signal processing applications, the input signals are readily known to be non-stationary with a non-Toeplitz covariance matrix. In this paper, we propose an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds while dealing with input signals that originate from a non-stationary process. In particular, the recovery methods are shown to accurately recover the time-varying variance and autocorrelation values. Furthermore, we extend the formulation of the Bussgang law to the case where non-stationary input signals are considered.

Robust Quantized Sampled–Data Stabilization for a Class of Lipschitz Nonlinear Systems With Time–Varying Uncertainties

In this letter, a robust quantized sampled-data controller is provided for a class of nonlinear systems affected by time-varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled-data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input-to-state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi-global practical stability, with arbitrarily small final target ball, of the related quantized sampled-data closed-loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a priori known. The theory here developed includes also the cases of time-varying sampling intervals and of non-uniform quantization of the input/output channels as well as the stability analysis of the inter-sampling system behavior. The provided results are validated through an example of one-link manipulator.

A Time Synchronization Method Between FBG Deformation Measurement System and Airborne DPOS Based on Waveform Matching

The airborne Distributed Position and Orientation System (DPOS) is an important means for multi-point motion measurement required for earth observation with multi-task sensing loads. The sub-nodes in DPOS rely on the main node to perform transfer alignment for them to get high-precision motion data, which requires accurate deformation data and the relative motion relationship between different nodes. Fiber Bragg Grating (FBG) is one of the main means of deformation measurement at present. However, the time synchronization error between FBG and DPOS directly restricts the accuracy of transfer alignment. For this, a high-precision time synchronization method based on waveform matching is presented. Firstly, the data correlation between FBG and DPOS is analyzed. Then the main time error factors, sampling frequency and time delay are determined. On this basis, the empirical mode decomposition and wavelet analysis are used to extract and match the vibration data from the FBGS and bending angle data calculated by DPOS, thus updating the time-varying sampling frequency and time delay of FBGS, and finally achieving high-precision time synchronization between FBGS and DPOS. Results of ground dynamic experiment show that the standard deviation and mean value of FBG time error is less than 4ms and 2ms respectively, and the deformation displacement error of synchronized FBG data is less than 1%, which provides a prerequisite for high-precision transfer alignment of DPOS.

Dynamic output feedback control for networked systems with limited communication based on deadband event-triggered mechanism

In this paper, a deadband event-triggered mechanism is used to reduce the transmission data of the network channel to improve the performance of networked control systems (NCSs) with limited communication. In view of the unmeasurable state signal in the actual network system, the dynamic output feedback control problem for the NCSs is studied. When network-induced delays, time-varying sampling intervals and signal transmission deadbands are considered simultaneously, the model of NCSs under the deadband event-triggered mechanism is constructed, and a sufficient condition for the stability of NCSs is given. Furthermore, the design method of the dynamic output feedback controller of NCSs under deadband event-triggered mechanism is proposed. Two simulation examples are used to show that the proposed approach can obtain the dynamic output feedback controller for NCSs with the deadband event-triggered mechanism, and also illustrate the deadband event-triggered mechanism can reduce the signal transmission in the network channel to obtain better system performance.